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Q. 11

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The Practice of Statistics for AP Examination

Found in: Page 455

Book edition 6th

Author(s) Daren Starnes, Josh Tabor

Pages 837 pages

ISBN 9781319113339

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Short Answer

Doing homework A school newspaper article claims that $60 %$ of the students at a large high school completed their assigned homework last week. Assume that this claim is true for the $2000$ students at the school.
a. Make a bar graph of the population distribution.
b. Imagine one possible SRS of size $100$ from this population. Sketch a bar graph of the distribution of sample data.

a. The bar graph :

b. The bar graph is

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part(a) Step 1 : Given information

We need to make bar graph for the students doing homework or not.

Part(a) Step 2 : Simplify

As we know, $60 %$ student completed homework. Therefore,

$100 % - 60 % = 40 %$ students did not complete their work.

So, in bar graph the width of bars will be equal and height of bars should be equal to their percentage.

The bar graph is

Part(b) Step 1 : Given information

We need to draw bar graph for one possible SRS of $100$ from total population.

Part(b) Step 2 : Simplify

As we know,

60 %

students completed their work. Now,

We have $100$ students in a random sample, so it means nearly $60 %$ students did their work but not exact $60$ .

Lets take an example , it is possible that $57$ students did their work.

Now, the width of bar graphs would be same and height will be equal to their respective frequencies.

The frequency bar graph is :

Most popular questions for Math Textbooks

The number of undergraduates at Johns Hopkins University is approximately 2000 , while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about $3 %$ of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80 at both schools. Which of the following is the best conclusion?

a. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it comes from a smaller population.

b. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it is based on a smaller sample size.

c. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it comes from a larger population.

d. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it is based on a larger sample size.

e. We expect that the estimate from Johns Hopkins will be about the same distance from the truth as the estimate from Ohio State because both samples are 3 % of their populations.

The distribution of scores on the mathematics part of the SAT exam in a recent year was approximately Normal with mean 515 and standard deviation 114 . Imagine choosing many SRSs of 100 students who took the exam and averaging their SAT Math scores. Which of the following are the mean and standard deviation of the sampling distribution of $x^{-}$ ? $\bar{x}$ ?

a. Mean $= 515, SD = 114$

b. Mean $= 515, SD = 114 / 100^{SD} = 114 / \sqrt{100}$

c. Mean role="math" localid="1654342976765" $= 515 / 100, SD = 114 / 100$

d. Mean role="math" localid="1654343050312" $= 515 / 100, SD = 114 / 100 SD = 114 / \sqrt{10}$

e. Cannot be determined without knowing the 100 scores.

Records from a dairy farm yielded the following information on the number of male and female calves born at various times of the day.

What is the probability that a randomly selected calf was born in the night or was a female?

a. $\frac{369}{513}$

b. $\frac{485}{513}$

C. $\frac{116}{513}$

d. $\frac{116}{252}$

e $^{\frac{116}{233}}$

A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability $\frac{1}{5}$ of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. What would be a proper way to use a table of random digits to do this?

a. One digit from the random digit table simulates one answer, with 5 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

b. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

c. One digit from the random digit table simulates one answer, with odd = correct and even = incorrect. Ten digits from the table simulate 10 answers.

d. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect, ignoring repeats. Ten digits from the table simulate 10 answers.

e. Two digits from the random digit table simulate one answer, with 00 to 20 = correct and 21 to 99 = incorrect. Ten pairs of digits from the table simulate 10 answers.

Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The standard deviation of the sampling distribution will decrease as the sample size increases.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.

c. The sample mean is an unbiased estimator of the population mean.

d. The sampling distribution shows how the sample mean is distributed around the population mean.

e. The sampling distribution shows how the sample is distributed around the sample mean.

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